If S is a Krull monoid with finitely generated divisor class group such that only finitely many divisor classes of S contain prime divisors, then we construct an algorithm to compute the elasticity of S. © 2001 Elsevier Science Inc. All rights reserved. AMS classification: 20M14; 20M25; 13F05; 11Y05

In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings an integral domain $D$. We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ simultaneously P$v$MDs (resp., Krull, G-GCD, Noetherian, Strong Mori). A complete characterization when a pullback is P$v$MD GCD, Mori, Mori) given. As corollaries, investigate...

Krull-Schmidt categories are additive categories such that each object decomposes into a finite direct sum of indecomposable objects having local endomorphism rings. We provide a self-contained introduction which is based on the concept of a projective cover.